Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2020; 35(2): 685-695

Online first article March 10, 2020      Printed April 30, 2020

https://doi.org/10.4134/CKMS.c190119

Copyright © The Korean Mathematical Society.

Kink wave solutions to KdV-Burgers equation with forcing term

Yusuf Buba Chukkol, Mukhiddin Muminov

Universiti Teknologi Malaysia; Universiti Teknologi Malaysia

Abstract

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In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

Keywords: KdVB equation, Riccati equation, secant hyperbolic ansatz, modified tanh-coth method

MSC numbers: 35Q53, 35Q51, 35L75

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